# Math Help - Group Theory: Proof on abelian and isomorphic groups.

1. ## Group Theory: Proof on abelian and isomorphic groups.

If a function f, defined f(g)=g^-1 maps a group G to G, is isomorphic, then G is abelian.

How do I go about proving this one?

2. Let $a,b\in G$, then

$ab=f((ab)^{-1})=f(b^{-1}a^{-1})=f(b^{-1})f(a^{-1})=ba$

thus G is abelian